IJRET: International Journal of Research in Engineering and Technology
eISSN: 2319-1163 | pISSN: 2321-7308
MODAL ANALYSIS OF A SIMPLY SUPPORTED SANDWICH BEAM Tukaram Zore1, Saurabh Singh2, Sunil Gaonkar3, Neena Panandikar4 1
B.E Mechanical Department, Padre Conceicao College of Engineering College, Goa, India B.E, Mechanical Department, Padre Conceicao College of Engineering College, Goa, India 3 B.E, Mechanical Department, Padre Conceicao College of Engineering College, Goa, India 4 Associate Professor, Mechanical Department, Padre Conceicao College of Engineering College, Goa, India 2
Abstract Every mechanical structure exhibits natural modes of vibration. Beams with variable cross section and material properties are frequently used in aeronautical, mechanical and civil engineering. Given the elastic and inertia characteristics of the structures, modes of vibration can be computed, the study being known as modal analysis. This paper presents modal analysis of simply supported beam using different materials. Comparison of natural frequency of the beam considering various materials is done analytically and also using ANSYS APDL. Effect of change of length and cross sectional area on natural frequency is also studied. Comparative study on natural frequency of sandwich beam using various materials is done analytically and also using ANSYS APDL.
Key words: Natural Frequency, Mode Shape, Sandwich Beam. -----------------------------------------------------------------------***------------------------------------------------------------------1. INTRODUCTION Vibration is mechanical phenomenon whereby oscillations occur about the equilibrium point. The oscillations may be periodic such as the motion of pendulum or random such as the motion of tire on gravel road. Every structure which is designed is subjected to some amount of vibrations. Unwanted vibrations may cause loosening of parts and cause accidents or heavy loss.[1] Mostly all materials exhibit some amount of internal structural damping. Most of the time it is not substantially effective to minimize the vibration around resonant frequencies.[3].Due to faulty design and poor manufacturing there is unbalanced and unpleasant stresses developed and creating unwanted noise. Careful designing usually minimize unwanted vibrations. Hence keeping in view all useful and devastating effects of the vibrations the study of the vibration is of immense importance. [1].
2. THEORITICAL ASPECTS
V and M are the shear and bending moments respectively, and p(x) represents the loading per unit length of the beam. The equation for the lateral vibration of the beam reduces to )) - ρ
(EI (
=0
In the special case where the flexure rigidity EI is a constant, the preceding equation can be written as : )-ρ
EI (
=0
On substituting β4= ρ
/EI
We obtain the fourth order equation
(
) -β4y=0 for the vibration of uniform beam
The natural frequencies of vibration are found from equation (3) to be
= Fig-1: Forces and moments acting on beam element To determine the differential equation for the lateral vibrations of beams, consider the forces and moments acting on an element of the beam shown in figure 1
2
=(
Where, the constant of the problem.
l)2 depends on the boundary conditions
2.1 Derivation to find βn value: Considering general equation
_______________________________________________________________________________________ Volume: 05 Issue: 06 | Jun-2016, Available @ http://ijret.esatjournals.org
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